Motif distribution, dynamical properties, and computational performance of two data-based cortical microcircuit templates☆
Introduction
Many complex networks from biochemistry and neurobiology as well as engineering share certain global properties (Newman, 2003, Strogatz, 2001, Watts and Strogatz, 1998), like degree distributions (distribution of the number of edges per node) and small-world properties, i.e. local clustering of edges in a graph while maintaining a short path between nodes. But they often have different local properties, yielding different distributions of stereotypical connectivity patterns for few nodes, called motifs (Milo et al., 2002, Milo et al., 2004, Shen-Orr et al., 2002).
Neurobiological studies have shown that cortical circuits have a distinctive modular and laminar structure, with stereotypical connections between neurons that are repeated throughout many cortical areas (Douglas et al., 1995, Douglas and Martin, 2004, Kalisman et al., 2005, Mountcastle, 1998, Nelson, 2002, Silberberg et al., 2002, White, 1989). It has been conjectured that these stereotypical canonical microcircuits are not merely an artifact of the specific mapping of afferent and efferent cortical pathways or other anatomical constraints like evolutionary processes or development, but are also advantageous for generic computational operations that are carried out throughout the neocortex.
Over the past years detailed statistical data became available that are based on two different experimental methods: dual intracellular recordings in vitro and cell morphology. The first dataset assembled by Thomson et al. (2002) was estimated from 998 paired intracellular recordings with sharp electrodes in slices of somatosensory, motor and visual areas of adult rats and adult cats. It specifies connection probabilities and connection strengths of effectively established synaptic connections between excitatory and inhibitory neocortical neurons, to which we will refer as functional connectivity in this paper. The second dataset assembled by Binzegger et al. (2004) was predicted from bouton and target densities in cat primary visual cortex estimated from three-dimensional cell reconstructions. This dataset does not specify the distribution of functional connections, but rather represents potential synaptic connectivity. The probabilities of synaptic connections between excitatory and inhibitory neurons located in different layers, i.e. layer 2/3, 4 and 5, differ significantly for the functional and the potential microcircuit template (see Thomson and Lamy, 2007). In addition this dataset also includes neurons in layer 6.
We investigate these two cortical microcircuit templates with regard to structural and functional properties. In order to evaluate the computational properties of microcircuit templates we carried out computer simulations of detailed cortical microcircuit models consisting of 560 Hodgkin–Huxley type point neurons and synaptic connections with stereotypical dynamic properties (such as paired pulse depression and paired pulse facilitation) from Markram et al. (1998). Similar to Häusler and Maass (2007), our analysis is based on the assumption that stereotypical cortical microcircuits have some “universal” computational capabilities, and can support quite different computations in different cortical areas. Consequently we concentrate on generic information processing capabilities that are likely to be needed for many concrete computational tasks: to accumulate, hold and fuse information contained in Poisson input spike trains from two different sources (modeling thalamic or cortical feedforward input that arrives primarily in layer 4, and lateral or top-down input that arrives primarily in layer 2/3). In addition we examine the capability of such circuit models to carry out linear and nonlinear computations on time-varying firing rates of these two afferent input streams. In order to avoid rather arbitrary assumptions about the specific type of neuronal encoding of the results of such computations, we analyzed how much information is available about the results of such computations to the generic “neural users”, i.e., to pyramidal neurons in layer 2/3 (which typically project to higher cortical areas) and to pyramidal neurons in layer 5 (which typically project to lower cortical areas or to subcortical structures, but also project for example from V1 back to nonspecific thalamus, i.e. to the intralaminar and midline nuclei that do not receive direct primary sensory input, and through this relay to higher cortical areas, see Callaway (2004)).
In Häusler and Maass (2007) it was shown that the cortical microcircuit model based on the template from Thomson et al. (2002) exhibits specific computational advantages over various types of control circuits that have the same components and the same global statistics of neurons and synaptic connections, but are missing the lamina-specific structure of real cortical microcircuits. Furthermore it was demonstrated that the connectivity graphs defined by this cortical microcircuit template has a small-world property. However we had shown that the degree distribution of neurons is more salient for their computational performance than the small world property.
Here we extend this study by showing that the two cortical microcircuit templates of Thomson et al., 2002, Binzegger et al., 2004 share some global structural properties, like degree distributions and small-world properties, but have significantly different local structural properties, i.e. network motif distributions. A comparison of the information processing capabilities of both microcircuit templates reveals that they have a similar average computational performance but significantly different computational properties for specific tasks. We also address the question which aspect of the microcircuit template of Binzegger et al. (2004) is essential for its computational performance, by scrambling specific aspects of their connectivity pattern in a variety of control circuits. We find that, like for the template of Thomson et al. (2002), the degree distribution of nodes is essential for its computational performance. This result is, besides their similar average computational performance, a second common property of these otherwise quite dissimilar microcircuit templates. We also identify specific properties of the dynamics of the two networks that correlate with their superior computational performance.
Section snippets
Microcircuits and computational tasks
We analyzed cortical microcircuit models based on the laminae-specific connectivity pattern specified by two different cortical microcircuit templates. The first cortical microcircuit template assembled by Thomson et al. (2002) was estimated from paired intracellular recordings with sharp electrodes from 998 pairs of identified neurons from somatosensory, motor and visual areas of adult rats, and visual areas of adult cats. The sampling was made randomly within a lateral spread of (
Graph properties of the two microcircuit templates
We analyzed the two data-based cortical microcircuit templates9 shown in Fig. 1, Fig. 2 for their differences and similarities in connectivity structure. In order to evaluate the significance of specific structural features of the two data-based microcircuit templates we compared them with random control circuits which consist of the same number of components, i.e. neurons
Discussion
We found that (1) the microcircuit template by Binzegger et al. (2004) and the microcircuit template by Thomson et al. (2002) have significant small-world properties, but quite different motif distributions; (2) both data-based microcircuits have similar circuit dynamics and average computational capabilities but different computational properties for individual tasks; and (3) the degree distribution is the aspect of the connectivity structure of both data-based microcircuit templates that is
Conclusions
This article has shown that the two available templates for cortical microcircuits have quite interesting structural, dynamical, and computational features. In particular we have shown that it is possible to relate the structure and the (conjectured) computational function of these two microcircuit templates. This positive result will hopefully stimulate further systematic experimental work on the anatomy and physiology of cortical microcircuits, that is needed in order to arrive at a definite
Acknowledgements
We would like to thank Tom Binzegger, Rolf Kötter, Henry Markram, Olaf Sporns, and Alex Thomson for helpful discussions on research related to this article. We also would like to thank two anonymous referees for helpful comments.
References (46)
Feedforward, feedback and inhibitory connections in primate visual cortex
Neural Networks
(2004)- et al.
Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons
Neuroscience
(2001) Cortical microcircuits: diverse or canonical?
Neuron
(2002)- et al.
Stereotypy in neocortical microcircuits
Trends Neurosci.
(2002) An Introduction to Systems Biology: Design Principles of Biological Circuits
(2006)- et al.
Power spectrum analysis of bursting cells in area MT in the behaving monkey
J. Neurosci.
(1994) - et al.
Does the 1/f frequency scaling of brain signals reflect self-organized critical states?
Phys. Rev. Lett.
(2006) - et al.
A quantitative map of the circuit of cat primary visual cortex
J. Neurosci.
(2004) - et al.
Laminar sources of synaptic input to cortical inhibitory interneurons and pyramidal neurons
Nature Neurosci.
(2000) - et al.
Spatiotemporal analysis of local field potentials and unit discharges in cat cerebral cortex during natural wake and sleep states
J. Neurosci.
(1999)
Recurrent excitation in neocortical circuits
Science
Neuronal circuits of the neocortex
Annu. Rev. Neurosci.
Memory traces in dynamical systems
PNAS USA
Relative contributions of burst and tonic responses to the receptive field properties of lateral geniculate neurones in the cat
J. Neurophysiol.
Response latencies of cells in the cats lateral geniculate neurones are less variable during burst than tonic firing
Visual Neurosci.
Organizing principles for a diversity of GABAergic interneurons and synapses in the neocortex
Science
A statistical analysis of information processing properties of lamina-specific cortical microcircuit models
Cerebral Cortex
Pyramidal cell communication within local networks in layer 2/3 of rat neocortex
J. Physiol.
Spatial growth of real-world networks
Phys. Rev. E
The neocortical microcircuit as a tabula rasa
Proc. Natl. Acad. Sci.
Cortical feed-forward networks for binding different streams of sensory information
Nature Neurosci.
Simple Markov-chain algorithms for generating bipartite graphs and tournaments
Random Struct. Algorithms
Real-time computing without stable states: a new framework for neural computation based on perturbations
Neural Comput.
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Written under partial support by the Austrian Science Fund FWF # S9102-N13 and project # FP6-015879(FACETS), project # FP7-216593 (SECO), project # FP7-506778 (PASCAL2) as well as project # FP7-231267 (ORGANIC) of the European Union.